In one of the contests I came across the following problem: Given n points (x,y) where n<=3*10^5 and |x|,|y|<=10^9.You need to find such point M(x',y') that if you look from that point on any of the given points and then rotate 180 degrees — you will also see point from the given set(on the same distance). Basically, M is the symmetry point. This task wasn't hard to solve, but because I haven't read the text carefully, at first I was trying to solve more generalized version: Find(if it exists) such point M that for every point from the set there is another point which is on the other "side"(you will see it if you rotate 180 degrees and no matter if it has another distance from M). Is there any solution for this problem? At least O(n^2)?